77,100 research outputs found

    Parameter Estimation and Uncertainty Quantication for an Epidemic Model

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    We examine estimation of the parameters of Susceptible-Infective-Recovered (SIR) models in the context of least squares. We review the use of asymptotic statistical theory and sensitivity analysis to obtain measures of uncertainty for estimates of the model parameters and the basic reproductive number (R0 )ā€”an epidemiologically signiļ¬cant parameter grouping. We ļ¬nd that estimates of diļ¬€erent parameters, such as the transmission parameter and recovery rate, are correlated, with the magnitude and sign of this correlation depending on the value of R0. Situations are highlighted in which this correlation allows R0 to be estimated with greater ease than its constituent parameters. Implications of correlation for parameter identiļ¬ability are discussed. Uncertainty estimates and sensitivity analysis are used to investigate how the frequency at which data is sampled aļ¬€ects the estimation process and how the accuracy and uncertainty of estimates improves as data is collected over the course of an outbreak. We assess the informativeness of individual data points in a given time series to determine when more frequent sampling (if possible) would prove to be most beneļ¬cial to the estimation process. This technique can be used to design data sampling schemes in more general contexts

    Mapping the disease-specific LupusQoL to the SF-6D

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    Purpose To derive a mapping algorithm to predict SF-6D utility scores from the non-preference-based LupusQoL and test the performance of the developed algorithm on a separate independent validation data set. Method LupusQoL and SF-6D data were collected from 320 patients with systemic lupus erythematosus (SLE) attending routine rheumatology outpatient appointments at seven centres in the UK. Ordinary least squares (OLS) regression was used to estimate models of increasing complexity in order to predict individualsā€™ SF-6D utility scores from their responses to the LupusQoL questionnaire. Model performance was judged on predictive ability through the size and pattern of prediction errors generated. The performance of the selected model was externally validated on an independent data set containing 113 female SLE patients who had again completed both the LupusQoL and SF-36 questionnaires. Results Four of the eight LupusQoL domains (physical health, pain, emotional health, and fatigue) were selected as dependent variables in the final model. Overall model fit was good, with R2 0.7219, MAE 0.0557, and RMSE 0.0706 when applied to the estimation data set, and R2 0.7431, MAE 0.0528, and RMSE 0.0663 when applied to the validation sample. Conclusion This study provides a method by which health state utility values can be estimated from patient responses to the non-preference-based LupusQoL, generalisable beyond the data set upon which it was estimated. Despite concerns over the use of OLS to develop mapping algorithms, we find this method to be suitable in this case due to the normality of the SF-6D data

    Growth Economics and Reality

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    This paper questions current empirical practice in the study of growth. We argue that much of the modern empirical growth literature is based on assumptions concerning regressors, residuals, and parameters which are implausible both from the perspective of economic theory as well as from the perspective of the historical experiences of the countries under study. A number of these problems are argued to be forms of violations of an exchangeability assumption which underlies standard growth exercises. We show that relaxation of these implausible assumptions can be done by allowing for uncertainty in model specification. Model uncertainty consists of two types: theory uncertainty, which relates to which growth determinants should be included in a model, and heterogeneity uncertainty, which relates to which observations in a data set comprise draws from the same statistical model. We propose ways to account for both theory and heterogeneity uncertainty. Finally, using an explicit decision-theoretic framework, we describe how one can engage in policy-relevant empirical analysis.

    Some recent developments in microeconometrics: A survey

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    This paper summarizes some recent developments in rnicroeconometrics with respect to methods for estimation and inference in non-linear models based on cross-section and panel data. In particular we discuss recent progress in estimation with conditional moment restrictions, simulation methods, serniparametric methods, as well as specification tests. We use the binary cross-section and panel probit model to illustrate the application of some of the theoretical results. --
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